A tight upper bound for the number of intersections between two rectangular paths

The problem of finding the number of intersections between two geometric figures in the plane has been studied extensively in literature. In this paper, the geometric figure comprising a continuous rectilinear path (called rectangular path) is considered, and a tight (least) upper bound onI(P, Q), the number of intersections between two rectangular pathsP andQ, is given.Editors' Note: One of our referees has reported that the main result of this paper has recently been given independently by a Chinese researcher at the University of Science and Technology, Hefei, P. R. of China. His paper is under publication in the Chinese Science Bulletin. However, since this journal may not be easily accessible to our readers, and further the two papers are obviously independent of each other, theBIT Editors have decided to accept the present paper.     

Solution/Ammonolysis Syntheses of Unsupported and Silica-Supported Copper(I) Nitride Nanostructures from Oxidic Precursors

Herein we describe an alternative strategy to achieve the preparation of nanoscale Cu₃N. Copper(II) oxide/hydroxide nanopowder precursors were successfully fabricated by solution methods. Ammonolysis of the oxidic precursors can be achieved essentially pseudomorphically to produce either unsupported or supported nanoparticles of the nitride. Hence, Cu₃N particles with diverse morphologies were synthesized from oxygen-containing precursors in two-step processes combining solvothermal and solid−gas ammonolysis stages. The single-phase hydroxochloride precursor, Cu₂(OH)₃Cl was prepared by solution-state synthesis from CuCl₂·2H₂O and urea, crystallising with the atacamite structure. Alternative precursors, CuO and Cu(OH)₂, were obtained after subsequent treatment of Cu₂(OH)₃Cl with NaOH solution. Cu₃N, in the form of micro- and nanorods, was the sole product formed from ammonolysis using either CuO or Cu(OH)₂. Conversely, the ammonolysis of dicopper trihydroxide chloride resulted in two-phase mixtures of Cu₃N and the monoamine, Cu(NH₃)Cl under similar experimental conditions. Importantly, this pathway is applicable to afford composite materials by incorporating substrates or matrices that are resistant to ammoniation at relatively low temperatures (ca. 300 °C). We present preliminary evidence that Cu₃N/SiO₂ nanocomposites (up to ca. 5 wt.% Cu₃N supported on SiO₂) could be prepared from CuCl₂·2H₂O and urea starting materials following similar reaction steps. Evidence suggests that in this case Cu₃N nanoparticles are confined within the porous SiO₂ matrix.     

草酸根桥联的Cu_2~ⅡFe~Ⅲ、Ni_2~ⅡFe~Ⅲ、Co_2~ⅡFe~Ⅲ异三核配合物的合成、表征及抗菌活性

合成了 7种草酸根桥联的 Cu 2 Fe 、Ni 2 Fe 、Co 2 Fe 异三核配合物 [M2 Fe(C2 O4) 3Lx](Cl O4) ,(M=Cu,L=bpy,Me2 phen,NO2 phen,x=2 ;M=Ni,Co,L=bpy,Me2 phen,x=4 ) .经元素分析、摩尔电导和磁性的测定以及红外光谱和电子光谱等方法对这些配合物进行了表征 ,确定了配合物的组成和结构 .初步生物活性试验表明形成异三核配合物后其杀菌活性明显提高     

Multi-quark structure ofU(3.1)

We interpret the recently observedU(3.1) mesons with the \(\Lambda \bar p\) + pions decays as the bound state of \(\Lambda ,\bar p\) andX ₀(1480). TheX ₀(1480) is a mesonium with \(Q^2 \bar Q^2 \) structures observed in γγ reactions and \(\bar pn\) annihilations. With this interpretation, we can understand its decay modes. Furthermore, we predict the ratio of \(\sigma (\Lambda \bar p\pi ^ + \pi ^ - )/\sigma (\Lambda \bar p\pi ^ + \pi ^ + )\) to be ?3.1 for centrally produced events and that the width of \(U^ - (\Lambda \bar p\pi ^ + \pi ^ - )\) to be greater than that of \(U^ + (\Lambda \bar p\pi ^ + \pi ^ + )\) . Both predictions seem to be in reasonable accord with the available data. We call for the detection of the \(\Lambda \bar p\pi ^ - \pi ^ - \) mode to verify the present interpretation.     

Preconcentration and separation of trace Pd(II) and Pt(IV) with silica gel bonded by aminopropyl-benzoylazo-4-(2-pyridyl-azo)-resorcinol

This paper reports a simple and highly selective method for preconcentrating and separating of trace Pd(II) and Pt(IV) with silica gel bonded by aminopropyl-benzoylazo-4-(2-pyridy-lazo)-resorcinol (ABPR-SG). ABPR-SG is stable in solution from 6 mol/L HCl to pH 7.0 and in common organic solvents. The maximum adsorptive capacity of Pd(n) on ABPR-SG is 362 μmol/g. After preconcentration and separation by using ABPR-SG column, Pd(II) and Pt(IV) of μg/L level in artificial water samples can be measured reliably by common spedrophotometry. The maximum concentration factors of Pd(II) and Pt(IV) on ABPR-SG column are 143 and 125 respectively. The chromatographic column packed with ABPR-SG can be reused. The method is simple and efficient.     

First and Second Order Optimality Conditions Using Approximations for Nonsmooth Vector Optimization in Banach Spaces

We use the first and second order approximations of mappings to establish both necessary and sufficient optimality conditions for unconstrained and constrained nonsmooth vector optimization problems. Ideal solutions, efficient solutions, and weakly efficient solutions are considered. The data of the problems need not even be continuous. Some often imposed compactness assumptions are also relaxed. Examples are provided to compare our results and some known recent results.This work was partially supported by the National Basic Research Program in Natural Sciences of Vietnam.     

具有位数3和4的双随机循环矩阵中的素元

本文研究了双随机循环矩阵中素元的分类问题．由于任一n阶双随机循环矩阵都可以唯一地表示为移位的n-1次一元多项式,从而可把双随机循环矩阵中素元的分类问题简化为解双随机循环矩阵上的一个方程．应用此原理,本文完全解决了判别具有位数3的n阶双随机循环矩阵是否为素元的问题,并给出了n阶双随机循环矩阵中一类具有位数4的素元．